If DD is not attending a school full-time, you can request an expedited hearing. Still a wait, but not a year.
Even if the LA has only named a type of placement, they are still responsible for ensuring DD receives a suitable full-time education and anything detailed, specified and quantified in F.
If the LA’s intention is to fulfil their duty to provide a suitable full-time education by DD attending the resource unit and DD is unable (in the legal sense) to attend, request alternative provision.
although it’s clear her needs are not mainstream which is supported by no mainstream accepting her
It isn’t quite as simple as this. It doesn’t matter how clear things are in actual terms. It matters what is on paper. B+F=I. If B&F are poor, there is a risk that a school that can meet needs on paper but not in real life will be named. This is why it is important to appeal B&F as well as I. And it is why evidence is important because B&F are based on evidence. Also, unless the schools are wholly independent, they don’t need to accept her. The LA, or SENDIST, can name them even if they object. Then they must admit. If the school believes one of the lawful exceptions to naming them applies and they are named anyway, they could challenge this, but they rarely do because they know the bar is far higher than LAs and schools like to believe.
You should try to gather evidence DD is unable to travel. It is possible to get evidence even if it is only you who drives her. Depending on the circumstances, a range of professionals can document travel difficulties, e.g. EP, OT, CP, psychiatrist, CAMHS nurse, social worker, GP, previous school… Yes, DD needs to be in a fit state to learn, but you need evidence.